Self-translational diffusion coefficient

The Dependencies of Radius of Gyration Rg, Static Correlation Length Hydrodynamic Screening Length Viscosity r, Self-Translational Diffusion Coefficient D, Cooperative Diffusion Coefficient Dc, Coupled Diffusion Coefficient Df, and Electrophoretic Mobility p on c and N for Various Regimes of Polyelectrolyte and Salt Concentrations... 

The self-translational diffusion coefficient D is related to f, by the Stokes-Einstein relation and is given by... 

But p decreases with salt concentration with an apparent exponent of k which changes from 0 at low salt concentration to — at high salt concentrations. The N-independence of p arises from a cancellation between hydrodynamic interaction and electrostatic coupling between the polyelectrolyte and other ions in the solution. It is to be noted that the self-translational diffusion coefficient D is proportional to as in the Zimm model with full... 

We have identified three diffusion coefficients. These are the self-translational diffusion coefficient D, cooperative diffusion coefficient Dc, and the coupled diffussion coefficient fly. fl is the cooperative diffusion coefficient in the absence of any electrostatic coupling between polyelectrolyte and other ions in the system, fly is the cooperative diffusion coefficient accounting for the coupling between various ions. For neutral polymers, fly and Dc are identical. Furthermore, we identify fly as the fast diffusion coefficient as measured in dynamic light scattering experiments. The fourth diffusion coefficient is the slow diffusion coefficient fl discussed in the Introduction. A satisfactory theory of flj is not yet available. 

In addition, by measuring the intensity fluctuations at low scattering angles changes in the translational diffusion coefficient can be measured during the early phases of self-assembly as illustrated by Figure 5.5. The translational diffusion coefficient decreases as the ratio of the length to width increases as linear assembly occurs. 

Figure 5.5. Measurement of physical properties during initiation of collagen self-assembly. Translation diffusion coefficient (D20-w) (top) and intensity of scattered light at 90° (bottom) versus time for type I collagen. Note translational diffusion constant decreases, whereas intensity of scattered light remains initially unchanged.

The zero mode is the self-diffusion of the center of mass whose diffusion coefficient is given by the Stokes-Einstein relation D = k TIN. The time Tj will be proportional to the time required for a chain to diffuse an end-to-end distance, that is, R )/D = t N b lk T. This means that for time scales longer than Tj the motion of the chain will be purely diffusive. On timescales shorter than Tj, it will exhibit viscoelastic modes. However, the dynamics of a single chain in a dilute solution is more complex due to long-range forces hydrodynamic interactions between distant monomers through the solvent are present and, in good solvents, excluded volume interactions also have to be taken into account. The correction of the Rouse model for hydrodynamic interaction was done by Zimm [79]. Erom a mathematical point of view, the problem becomes harder and requires approximations to arrive at some useful results. In this case, the translational diffusion coefficient obtained is... 

Diffusion. The translational diffusion coefficient D is the most commonly measured transport property of polymer solutions, but as there are several distinct types of diffusion, care must be taken to interpret D properly. For c < c, Brownian motion of isolated chains in a homogeneous solvent defines the dilute solution diffusion coefficient Dq. As c increases toward c and above, chain-chain interactions modify the friction felt during chain motion. Under these conditions, the tracer- or self-diffusion coefficient Dtr is measured by tracking the path of a single chain in a macroscopically imiform mixture of chains and solvent. To distinguish the test chain from neighbors so that its path can be identified, the chain... 

In dynamic LLS, the Laplace inversion of each measured intensity-intensity time correlation function G Hq,t) in the self-beating mode can lead to a line-width distribution GiF), where q is the scattering vector. For dilute solutions, Tis related to the translational diffusion coefficient D by iriq )g- o,c->-o A so that G(L) can be converted into a transitional diffusion coefficient distribution G D) or... 

In a liquid that is in thermodynamic equilibrium and which contains only one chemical species, the particles are in translational motion due to thermal agitation. The term for this motion, which can be characterized as a random walk of the particles, is self-diffusion. It can be quantified by observing the molecular displacements of the single particles. The self-diffusion coefficient is introduced by the Einstein relationship... 

PGSE-NMR provides direct information on the translational mobility of a liquid medium capable of swelling a given CFP. The self-diffusion coefficient of the swelling agent is found to be related to the nanoporosity of the matrix as determined from ISEC and to the rotational correlation time of a suitable paramagnetic probe (ESR) [22]. 

To summarize, there is a sizable and self-consistent body of data indicating that rotational and translational mobility of molecules inside swollen gel-type CFPs are interrelated and controlled mainly by viscosity. Accordingly, T, self-diffusion and diffusion coefficients bear the same information (at least for comparative purposes) concerning diffusion rates within swollen gel phases. However, the measurement of r is by far the most simple (it requires only the collection of a single spectrum). For this reason, only r values have been used so far in the interpretation of diffusion phenomena in swollen heterogeneous metal catalysts supported on CFPs [81,82]. 

NMR Self-Diffusion of Desmopressin. The NMR-diffusion technique (3,10) offers a convenient way to measure the translational self-diffusion coefficient of molecules in solution and in isotropic liquid crystalline phases. The technique is nonperturbing, in that it does not require the addition of foreign probe molecules or the creation of a concentration-gradient in the sample it is direct in that it does not involve any model dependent assumptions. Obstruction by objects much smaller than the molecular root-mean-square displacement during A (approx 1 pm), lead to a reduced apparent diffusion coefficient in equation (1) (10). Thus, the NMR-diffusion technique offers a fruitful way to study molecular interactions in liquids (11) and the phase structure of liquid crystalline phases (11,12). 

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